Students will learn how length contraction follows from time dilation and the meaning of the gamma factor.
An object moving with speed has a dimensionless speed calculated by dividing the speed by the speed of light ( ). .
The dimensionless Lorentz “gamma” factor can be calculated from the speed, and tells you how much time dilation or length contraction there is. .
If you see an object of length moving towards you at a Lorentz gamma factor , it will appear shortened (contracted) in the direction of motion to new length .
|Object||Speed (km/sec)||Lorentz Factor|
|Electron at the Stanford Linear Accelerator|
Watch this Explanation
Time for Practice
- What would be the Lorentz gamma factor for a space ship traveling at the speed of light c? If you were in this space ship, how wide would the universe look to you?
- How fast would you have to drive in your car in order to make the road % shorter through Lorentz contraction?
In 1987 light reached our telescopes from a supernova that occurred in a near-by galaxy
light years away. A huge burst of neutrinos preceded the light emission and reached Earth almost two hours ahead of the light. It was calculated that the neutrinos in that journey lost only
minutes of their lead time over the light.
- What was the ratio of the speed of the neutrinos to that of light?
- Calculate how much space was Lorentz-contracted form the point of view of the neutrino.
- Suppose you could travel in a spaceship at that speed to that galaxy and back. It that were to occur the Earth would be years older. How much would you have aged?
Answers to Selected Problems
- , the universe would be a dot